\newfont{\amsbold}{msbm10}
\newfont{\logobold}{logobf10 scaled\magstep2}
\newcommand{\real}{\mathbb{R}}
\newcommand{\assembly}{\mathop{\mbox{\logobold A}}}
\def\nsd{{n_\mathrm{sd}}}
\def\isd{{i_\mathrm{sd}}}
\def\nen{{n_\mathrm{en}}}
\def\nel{{n_\mathrm{el}}}
\def\iel{{i_\mathrm{el}}}
\def\nln{{n_\mathrm{ln}}}
\def\nq{{n_\mathrm{eq}}}
\def\nelem{{n_\mathrm{e}}}
\def\nnode{{n_\mathrm{n}}}
\def\ndf{{n_\mathrm{dof}}}
\def\idf{{i_\mathrm{dof}}}
\def\ned{{n_\mathrm{ed}}}
\def\nee{{n_\mathrm{ee}}}
\def\iee{{i_\mathrm{ee}}}
\def\nint{{n_\mathrm{int}}}
\def\nquad{{n_\mathrm{quad}}}
\def\iquad{{i_\mathrm{quad}}}
\def\neemax{n_\mathrm{ee\_max}}
\def\npes{{n_\mathrm{PEs}}}
\def\Ot{\Omega_t}
\def\Gt{\Gamma_t}
\def\On{\Omega_n}
\def\Gn{\Gamma_n}
\newcommand{\Reynolds}{\mathrm{Re}}
\newcommand{\Prandtl}{\mathrm{Pr}}
\newcommand{\Froude}{\mathrm{Fr}}
\newcommand{\Strouhal}{\mathrm{St}}
\def\sbn{{\pmb n}}
\def\sbt{{\pmb t}}
\def\sbb{{\pmb b}}
\newcommand{\ba}{\mathbf{a}}
\newcommand{\bb}{\mathbf{b}}
\newcommand{\bc}{\mathbf{c}}
\newcommand{\bd}{\mathbf{d}}
\newcommand{\be}{\mathbf{e}}
\newcommand{\force}{\mathbf{f}}
\newcommand{\bg}{{\boldsymbol{\mathit{g}}}}
\newcommand{\bh}{{\boldsymbol{\mathit{h}}}}
\newcommand{\bi}{\mathbf{i}}
\newcommand{\bj}{\mathbf{j}}
\newcommand{\bk}{\mathbf{k}}
\newcommand{\bm}{\mathbf{m}}
\newcommand{\bn}{\mathbf{n}}
\newcommand{\bp}{\mathbf{p}}
\newcommand{\bq}{\mathbf{q}}
\newcommand{\br}{\mathbf{r}}
\newcommand{\bs}{\mathbf{s}}
\newcommand{\bt}{\mathbf{t}}
\newcommand{\bu}{\mathbf{u}}
%\newcommand{\bu}{\tmmathbf{u}}
\newcommand{\bv}{\mathbf{v}}
\newcommand{\bw}{\mathbf{w}}
%\newcommand{\bw}{\tmmathbf{w}}
\newcommand{\bx}{\mathbf{x}}
\newcommand{\by}{\mathbf{y}}
\newcommand{\bz}{\mathbf{z}}
\newcommand{\bA}{\mathbf{A}}
\newcommand{\bB}{\mathbf{B}}
\newcommand{\bC}{\mathbf{C}}
\newcommand{\bD}{\mathbf{D}}
\newcommand{\bE}{\mathbf{E}}
\newcommand{\bF}{\mathbf{F}}
\newcommand{\bG}{\mathbf{G}}
\newcommand{\bH}{\mathbf{H}}
\newcommand{\bI}{\mathbf{I}}
\newcommand{\bJ}{\mathbf{J}}
\newcommand{\bK}{\mathbf{K}}
\newcommand{\bL}{\mathbf{L}}
\newcommand{\bM}{\mathbf{M}}
\newcommand{\bN}{\mathbf{N}}
\newcommand{\bO}{\mathbf{O}}
\newcommand{\bP}{\mathbf{P}}
\newcommand{\bQ}{\mathbf{Q}}
\newcommand{\bR}{\mathbf{R}}
\newcommand{\bS}{\mathbf{S}}
\newcommand{\bT}{\mathbf{T}}
\newcommand{\bU}{\mathbf{U}}
\newcommand{\bV}{\mathbf{V}}
\newcommand{\bW}{\mathbf{W}}
\newcommand{\bX}{\mathbf{X}}
\newcommand{\bY}{\mathbf{Y}}
\newcommand{\bZ}{\mathbf{Z}}
\newcommand{\zero}{\mathbf{0}}
\newcommand{\bxi}{{\boldsymbol{\xi}}}
\newcommand{\balpha}{{\boldsymbol{\alpha}}}
\newcommand{\bomega}{{\boldsymbol{\omega}}}
\newcommand{\bchi}{{\boldsymbol{\chi}}}
\newcommand{\btheta}{{\boldsymbol{\theta}}}
%\newcommand{\bChi}{{\boldsymbol{\Chi}}}
\newcommand{\bepsilon}{{\boldsymbol{\epsilon}}}
\newcommand{\bPsi}{{\boldsymbol{\Psi}}}
\newcommand{\bphi}{{\boldsymbol{\phi}}}
\newcommand{\bpi}{{\boldsymbol{\pi}}}
\newcommand{\design}{\balpha}
\def\but{{\bf u}_{,t}}
\def\bvt{{\bf v}_{,t}}
\def\ST{{{\cal S}^h_\bT}}
\def\VT{{{\cal V}^h_\bT}}
\def\SH{{{\cal S}^h_H}}
\def\VH{{{\cal V}^h_H}}
\def\Su{{{\cal S}^h_\bu}}
\def\Vu{{{\cal V}^h_\bu}}
\def\SU{{{\cal S}^h_\bU}}
\def\VU{{{\cal V}^h_\bU}}
\def\Sv{{{\cal S}^h_\bv}}
\def\Vv{{{\cal V}^h_\bv}}
\def\Sp{{{\cal S}^h_p}}
\def\Vp{{{\cal V}^h_p}}
\def\Sh{{{\cal S}^h_\phi}}
\def\Vh{{{\cal V}^h_\phi}}
\def\Sun{{(\Su)_n}}
\def\Vun{{(\Vu)_n}}
\def\SHn{{(\SH)_n}}
\def\VHn{{(\VH)_n}}
\def\SUn{{(\SU)_n}}
\def\VUn{{(\VU)_n}}
\def\Svn{{(\Sv)_n}}
\def\Vvn{{(\Vv)_n}}
\def\Spn{{(\Sp)_n}}
\def\Vpn{{(\Vp)_n}}
\def\Shn{{(\Sh)_n}}
\def\Vhn{{(\Vh)_n}}
\newcommand{\strain}{{\boldsymbol{\epsilon}}}
\newcommand{\stress}{{\boldsymbol{\sigma}}}
\newcommand{\blambda}{{\boldsymbol{\lambda}}}
\renewcommand{\div}{{\boldsymbol{\nabla}}}
\newcommand{\sbg}{\bg}
\newcommand{\sbh}{\bh}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\tauT}{{\tau_\mathrm{\scriptscriptstyle CONS}}}
\newcommand{\tauu}{{\tau_\mathrm{\scriptscriptstyle MOM}}}
\newcommand{\taup}{{\tau_\mathrm{\scriptscriptstyle CONT}}}
\newcommand{\taudc}{{\tau_\mathrm{\scriptscriptstyle DC}}}
\newcommand{\tauadv}{{\tau_\mathrm{\scriptscriptstyle ADV}}}
\newcommand{\tausupg}{{\tau_\mathrm{\scriptscriptstyle SUPG}}}
\newcommand{\taupspg}{{\tau_\mathrm{\scriptscriptstyle PSPG}}}
\newcommand{\taugls}{{\tau_\mathrm{\scriptscriptstyle GLS}}}
\newcommand{\tauglsa}{{\tau_\mathrm{\scriptscriptstyle GLS1}}}
\newcommand{\tauglsb}{{\tau_\mathrm{\scriptscriptstyle GLS2}}}
\newcommand{\oneovermu}{\frac{1}{2 \mu_{1}}}
\newcommand{\lamovermu}{\frac{\lambda}{2 \mu_{1}}}
\newcommand{\lsqovermu}{\frac{\lambda^{2}}{2 \mu_{1}}}
\newcommand{\hash}{{\includegraphics[width=0.1in]{x.ps}}}
\newcommand{\hashblue}{{\includegraphics[width=0.1in]{x-blue.ps}}}
\newcommand{\subhash}{{\includegraphics[width=0.06in]{x.ps}}}
\newcommand{\subhashblue}{{\includegraphics[width=0.06in]{x-blue.ps}}}
\newcommand{\upup}           {{\includegraphics[width=0.1in]{h.ps}}}
\newcommand{\upupblue}       {{\includegraphics[width=0.1in]{h-blue.ps}}}
\newcommand{\upupred}        {{\includegraphics[width=0.1in]{h-red.ps}}}
\newcommand{\upupmagenta}    {{\includegraphics[width=0.1in]{h-magenta.ps}}}
\newcommand{\subupup}        {{\includegraphics[width=0.1in]{h.ps}}}
\newcommand{\subupupblue}    {{\includegraphics[width=0.06in]{h-blue.ps}}}
\newcommand{\subupupred}     {{\includegraphics[width=0.06in]{h-red.ps}}}
\newcommand{\subupupmagenta} {{\includegraphics[width=0.06in]{h-magenta.ps}}}
